154 CHEMICAL ENGINEERING
(during the test) expressed as a percentage of the full outlet, As the majority of fan problems require solution on a basis of static pressure or maintained resistance rather than on a percentage of full outlet (a laboratory condition), Fig. 3 proves of greater utility. A curve of "discharge opening in percentage of full outlet" could be plotted on Fig. 3 as another ordinate against maintained resistance if desired.
Reduced Orifice.—This term is more common in European practice and is used as an abscissa against which are plotted volumetric, manometric and mechanical efficiencies. Reduced orifice is expressed by the equation Or = q/(r*-\/gH). Since this equation contains the factor r, it is evident that regardless of the size of fan of any given type the reduced orifice will be the same when the same relative restriction exists. This approaches the basis of Fig. 4, but instead of dealing with the percentage of opening of outlet, it deals with a value that is in reality some constant times the true percentage of full opening.
Equivalent Orifice.—This term is also more common in European practice and differs from "reduced orifice" in that the equation contains no term bearing on the proportions or size of the fan; hence the equivalent orifice is an actual quantity in square feet varying with the volume delivered. Equivalent orifice is expressed by the equation Oe = q/(K^/2gH). It represents the area of a circular hole in a thin plate which will produce a restricting effect equal to that which exists in the system under consideration regardless of the nature of the actual restriction. The value of K generally used ranges from 0.60 to 0.65, making Oe = q/Q&5\/2gH. It is more of a laboratory characteristic than one adaptable to general use.
Volumetric and manometric efficiency curves could be plotted, but the usefulness of such curves is limited. Volumetric efficiency is a direct function of the V/T-curve and may be represented by the product of V/T and a constant, the latter depending on the design of the fan. As the volume delivered at a given revolution per minute varies as D3, the volume per revolution = KiD*V/Tj and since the overall cubical content of the wheel is KzD3, the volumetric efficiency = KV/T, where K equals Ki/Kz. Ki and K2 depend on the design and proportions of the fan. The volumetric efficiency is maximum with free intake and discharge and runs as high as 400 to 500 per cent in fans of the multiblade type designed for high pressures at low peripheral speeds, while it runs as low as 100 per cent in fans designed for low pressures at high peripheral speeds. The manometric efficiency is generally highest when the outlet is closed and lowest when maximum volume is delivered. There are, however, types where the maximum value occurs at light loads varying from Y^ to J^ maximum volumetric delivery. In cased fans of the multiblade type the maximum efficiency (gH/Ci2) attained is about 150 per cent, while in open-running fans it is as low as 30 per cent. High mechanical efficiency (and generally high volumetric efficiency) is desirable, but with manometric efficiency it is usually the method of drive which determines the desirable value. The higher the speed of the driver the lower the manometric efficiency of the fan best adapted.to the drive.
Effects of Variations in Revolutions Per Minute, Volume, Pressure, Horsepower, Efficiency, Etc.—Where a given fan is operating with a given restriction on its inlet or outlet, the volume delivered will vary directly with the revolutions per minute (N), the various pressures as N2, and the air horsepower as N*. The mechanical efficiency will remain the same, therefore the brake horsepower will also vary as N3. The volume delivered by symmetrical fans will vary as D2 for any given peripheral speed of the wheel and resistance or static pressure. Under these conditions the mechanical efficiency remains constant, since the area of friction surfaces varies directly with the change in volume. The horsepower will therefore vary as D2. It is sometimes erroneously assumed that at very